docs: def standardized_mortality_ratio(e, b, s_e, s_b, n):
      """A utility function to compute standardized mortality ratio (SMR).
  
      Parameters
      ----------
      e          : array
                   (n*h, 1), event variable measured for each age group across n spatial units
      b          : array
                   (n*h, 1), population at risk variable measured for each age group across n spatial units
      s_e        : array
                   (n*h, 1), event variable measured for each age group across n spatial units in a standard population
      s_b        : array
                   (n*h, 1), population variable measured for each age group across n spatial units in a standard population
      n          : integer
                   the number of spatial units
  
      Notes
      -----
      e, b, s_e, and s_b are arranged in the same order
  
      Returns
      -------
      array
          (nx1)
  
      Examples
      --------
  
      Creating an array of an event variable (e.g., the number of cancer patients)
      for 2 regions in each of which 4 age groups are available.
      The first 4 values are event values for 4 age groups in the region 1,
      and the next 4 values are for 4 age groups in the region 2.
  
      >>> e = np.array([30, 25, 25, 15, 33, 21, 30, 20])
  
      Creating another array of a population-at-risk variable (e.g., total population)
      for the same two regions.
      The order for entering values is the same as the case of e.
  
      >>> b = np.array([100, 100, 110, 90, 100, 90, 110, 90])
  
      To compute standardized mortality ratio (SMR),
      we need two additional arrays for standard population and event.
      Creating s_e and s_b for standard event and population, respectively.
  
      >>> s_e = np.array([100, 45, 120, 100, 50, 30, 200, 80])
      >>> s_b = np.array([1000, 900, 1000, 900, 1000, 900, 1000, 900])
  
      Specifying the number of regions.
  
      >>> n = 2
  
      Applying indirect_age_standardization function to e and b
  
      >>> a, b = standardized_mortality_ratio(e, b, s_e, s_b, n)
      >>> round(a, 4)
      2.4869
      >>> round(b, 4)
      2.7368
  
      """
      s_r = s_e * 1.0 / s_b
      e_by_n = sum_by_n(e, 1.0, n)
      expected = sum_by_n(b, s_r, n)
      smr = e_by_n * 1.0 / expected
      return smr